Properties

Label 504.2.ca
Level 504
Weight 2
Character orbit ca
Rep. character \(\chi_{504}(5,\cdot)\)
Character field \(\Q(\zeta_{6})\)
Dimension 184
Newform subspaces 1
Sturm bound 192
Trace bound 0

Related objects

Downloads

Learn more about

Defining parameters

Level: \( N \) = \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 504.ca (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) = \( 504 \)
Character field: \(\Q(\zeta_{6})\)
Newform subspaces: \( 1 \)
Sturm bound: \(192\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(504, [\chi])\).

Total New Old
Modular forms 200 200 0
Cusp forms 184 184 0
Eisenstein series 16 16 0

Trace form

\( 184q - 2q^{4} - 6q^{6} - 2q^{7} - 2q^{9} + O(q^{10}) \) \( 184q - 2q^{4} - 6q^{6} - 2q^{7} - 2q^{9} - 6q^{10} + 12q^{12} - 18q^{14} - 2q^{15} - 2q^{16} + 12q^{18} - 6q^{22} - 6q^{23} - 12q^{24} + 78q^{25} - 6q^{26} - 8q^{28} + 7q^{30} - 6q^{33} + 6q^{34} + 22q^{36} - 33q^{38} - 8q^{39} - 18q^{40} - 42q^{42} - 9q^{44} + 2q^{46} - 12q^{47} + 9q^{48} - 2q^{49} + 9q^{50} + 21q^{52} + 33q^{54} + 18q^{56} + 4q^{57} - 3q^{58} - 59q^{60} + 12q^{62} - 72q^{63} - 8q^{64} - 42q^{66} - 18q^{68} - 27q^{70} + 12q^{72} - 12q^{73} - 57q^{74} + 12q^{76} + 19q^{78} - 4q^{79} - 57q^{80} - 18q^{81} + 69q^{84} - 27q^{86} - 6q^{87} + 9q^{88} - 24q^{89} - 75q^{90} - 36q^{92} - 45q^{96} - 45q^{98} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(504, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
\(a_2\) \(a_3\) \(a_5\) \(a_7\)
504.2.ca.a \(184\) \(4.024\) None \(0\) \(0\) \(0\) \(-2\)

Hecke Characteristic Polynomials

There are no characteristic polynomials of Hecke operators in the database